Thank you. I found is this:
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Acrobat Professional
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (*)
Version: 10.0
Platform: Windows
Registration Date: May 2, 2012
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(*) where x seems to be a number of a serial or key
Where can I download Acrobat X Pro and is that the key to activate it?
That's a good start. Pretty sure that it is. If you purchased it from Adobe, there is supposed to be a link to download along with the serial number. There is no official public download, and no replacements if you didn't buy from Adobe. Their policy has been to closedown old version downloads completely; you NEED to keep your installers.
However, I MIGHT have good news. Adobe have so many links they don't manage to close them all down, and this page has links to an old Adobe download (ON ADOBE'S SITE - this isn't a pirate copy). https://prodesigntools.com/adobe-acrobat-x-10-pro-reader-suite-direct-download-links-ddl.html There are complicated instructions about logging on, opening pages, and all sorts of things - follow them EXACTLY and don't skip any steps, no matter how weird or unnecessary they seem; don't jump straight to the download link as most people would do. Good luck - if you manage to get a copy, be sure to keep it!